binomial probability question

Factual Questions
21

Referring to my Problem introduced above:What if k = 0?. If N<=0, then P=0. Otherwise, P=1, since if we flip the coin, we’re guaranteed to have at least 0 tails. The boundary conditions should thus be

  1. P(N,k) = 0 if N<k or N<=0.
  2. P(N,k) = 1 if k<=0.
  3. P(k,k) = q^k if k>0.

For the dice problem of caffeine_overdose, a multinomial distribution is exactly what we’re looking for (as has been worked out above). If you’re going to deal with dice (or anything with more than a binary outcome) multinomials work great.

22

Actually, the simplest way to solve the die problem is to use a Markov chain. There are seven states, 0 through 6. When you’re in state n, you have a 5/6 probability of staying where you are, and a 1/6 chance of moving to state n + 1 (unless you’re in state 6–you always stay there). From there, it should be pretty simple to figure out how many rolls it should take you to get from state 0 to state 6.